During the night of August 31 a group of German soldiers, dressed as Poles, attack the German radio station in the border town of Gleiwitz. They have brought with them a German criminal, taken for the purpose from a concentration camp. They shoot him and leave his body as evidence of the night's dark deeds.

Berlin radio broadcasts to the world the news of this act of Polish aggression, together with details of the necessary German response. In the early hours of the morning of September 1 Hitler's tanks move into Poland. His planes take off towards Warsaw on the first bombing mission of a new European war.

After a final desperate day of diplomacy, attempting even at this late stage to find a peaceful solution, Chamberlain and Daladier each sends an ultimatum to Hitler. When no answer is received, both nations declare war on September 3.

The Polish army, airforce and civilian population put up a brave resistance to massive German force - increased, from September 17, by a Russian invasion from the east. Within a few weeks 60,000 Polish soldiers and 25,000 civilians die. By September 28 Warsaw has fallen. Poland is once again partitioned, with an eastern slice going to Russia (as so recently agreed in Moscow) and the lion's share to Germany.

Hitler's triumphs: 1939-1941

The rapid blitzkrieg against Poland is only the first of Hitler's extraordinary military successes during the opening eighteen months of the war. From the start he launches a vigorous and deadly U-boat campaign against Allied shipping in the Atlantic, but on land he allows his enemies and neutral neighbours a deceptive period of calm, in what becomes known as the Phoney War.

This is rudely shattered by his sudden attack on neutral Denmark and Norway in April 1940. German troops come onshore from warships and rapidly overrun both countries. It is a foretaste of even more dramatic events in western Europe a month later.

From May 10 German panzer divisions smash their to the coast through neutral Luxembourg, the Netherlands and Belgium. At the same time other divisions push west through northern France. British and French armies are trapped in a pincer movement at the coast. They escape only by means of the dramatic rescue achieved at Dunkirk.

Now the invasion force wheels south towards Paris. German troops enter the capital city on June 14. Two days later the French sue for peace. Hitler savours the moment of triumph, revenge for Germany's humiliation in 1918. He arrives in person to witness the signing of the armistice - and then goes sightseeing in Paris.

Britain is the next object of his attention. While German forces are assembled below for an invasion, Messerchmidts battle in the sky with British Spitfires and Hurricanes for control of the Channel. This encounter (the Battle of Britain, lasting from June to September 1940) is the first in the war to go against Hitler. It is a defeat in the sense that he fails to prevail, and therefore has to cancel his invasion plans. But from September he merely diverts his might against Britain in a different context - in the nightly pounding of British cities, which becomes known as the Blitz.

At this same period Hitler's U-boats, refuelling now on France's Atlantic coast, are sinking an ever greater tonnage of Allied merchant shipping in the Atlantic.

The first half of 1941 brings continuing success. Rommel, despatched by Hitler to take over the campaign in north Africa, pushes the British ever further back towards Egypt. At the same time a rapid German thrust south through the Balkans overwhelms Yugoslavia and drives the British out of mainland Greece (in April 1941) and Crete (in May).

Less than two years after the world war was provoked by his invasion of Poland, Hitler can look around at a Europe dominated by Germany. The situation is, to say the least, satisfactory. But his sudden invasion in June 1941 of his ally, Russia, introduces an unpredictable element.

A turning point: June-December 1941

The nations of continental Europe are now either neutral (Switzerland, Sweden), neutral but Fascist (Spain, Portugal), merged with Germany (Austria), occupied by Germany (Czechoslovakia, Poland, Luxembourg, Belgium, Netherlands, Denmark, Norway, most of France), forcibly neutralized (Vichy France), allied to Germany (Italy, USSR), suppressed by the USSR (Finland), or a patchwork of such conditions (Hungary and the Balkans).

For a dictator who found himself at war with the world a year or two earlier than he would have wished, it is an impressive achievement. The only failure has been the Battle of Britain, frustrating his plans to cross the Channel - but these were anyway somewhat half-hearted.

Admittedly in the very month when this situation is achieved, May 1941, there is one major setback. Germany's newest and most magnificent battleship, the Bismarck, has been launched earlier this year at Kiel. On her first sortie out of the Baltic she is spotted by the British navy. After doing much damage to the pack pursuing her, the vast ship is sunk on May 27 with the loss of nearly all her crew of 2222 sailors.

The state of the navy is a sore point between Hitler and his naval commander in chief, Erich Raeder. In the mid-1930s Hitler has assured Raeder, responsible for building up the fleet, that the coming war will not begin until 1944. Raeder therefore regards Germany's strength at sea as inadequate. After the loss of the Bismarck, his naval campaign focuses largely on U-boats.

If this is one of the significant turning points of 1941, two more are to follow before the end of the year. The first is Hitler's own doing. The second he has regarded as inevitable sooner or later. But together they will have a decisive effect on the outcome of the war.

The first involves Hitler's eastern policy. The USSR, the proselytizing force of world communism, has always been seen by Hitler as his main enemy. And it is to the east, through Poland and into the Ukraine, that his policy of Lebensraum and German expansion has been directed. An attack into these regions is part of his grand strategy. Hitler's skill has been to create the lull, with the Molotov-Ribbentrop pact, which enables him to secure his western flank before turning his attention eastwards.

In this strategy he is, in effect, carrying out the Schlieffen Plan which his predecessors in World War I had been unable to achieve. They failed in the first part of the plan, the conquest of France. With that behind him, Hitler is now ready to move on to stage two - the attack on Russia. His mistake, failing to learn the lesson of Napoleon's campaign, is to believe that this can be a quick affair (though he might reasonably expect the speed of motorized transport to make the difference).

When the first Russian winter is bringing home the harsh reality, the other great turning point of 1941 takes place without Hitler even being forewarned. His Japanese allies tell him nothing of their plan for a secret attack on the US fleet in Pearl Harbor on December 7.

The events of the second half of 1941 add four major powers to the cast list of the world war. Hitler has dragged in the USSR, just as Japan's action forces the full involvement of the USA. Japan herself, until now engaged only in a regional conflict with China, also becomes a new player on the global scene. And China, as Japan's enemy, is automatically now an ally of the western powers.

Thus by the end of 1941 the final alignment of the war is established, in terms of the major powers involved. The Allies are Britain and the Commonwealth, France, the USA, the USSR and China; the Axis powers are Germany, Italy and Japan. (In fact even this alignment is not yet quite final - in 1943 Italy changes sides.)

Ominous signs: 1941-1943

The failure to clinch the Russian campaign before the onset of winter in 1943 profoundly alarms Hitler's generals and would put the idea of a tactical withdrawal into the mind of anyone less obsessively obstinate than the Nazi leader. Yet Hitler's refusal to give an inch seems vindicated when the German armies are still in place to launch an aggessive new campaign on the eastern front during the summer of 1942.

By contrast in 1942-3 there are unmistakable reverses. In October 1942 the French forces in north Africa join the Allies. In January 1941 the entire German Sixth Army is captured at Stalingrad. In May, with the fall of Tunis, the Germans and Italians are driven out of north Africa. In September Italy surrenders unconditionally to the Allies.

Yet these disasters have the paradoxical effect of bringing Hitler even greater swathes of western Europe. The French action in north Africa enables him to sweep aside the armistice. His occupation of Vichy France brings the whole country into German hands. Similarly the Italian surrender, when the Allies are not yet much beyond Naples in their drive up the peninsula, leaves the whole of the rest of Italy under German control.

Although the tide of war has now turned, the autumn of 1943 gives Hitler the broadest canvas so far on which to create his vision of a new order. In his ideal world Germans will rule as a master race, inferior groups such as Slavs will be made use of as slave labour, and undesirables (Jews, Gypsies and Communists) will be exterminated.

Hitler's vision for Europe

These principles underlie the gradual development of the Nazis' murderous schemes. The appalling story unfolds in three separate stages.

Before the outbreak of war, with Germany and Austria exposed to the eyes of the world, persecution of Hitler's hated groups is limited to intimidation and violence. His underlying aim is to rid German territory of Jews by terrifying them into moving elsewhere. Visas to leave Germany are freely available, and the willingness to do so can even be enough to bring release from a concentration camp. By 1939 more than half the Jews in Germany and Austria have moved to other countries.

With the outbreak of war and the closing of borders, escape by emigration becomes difficult (though not at first absolutely impossible). And the German authorities are now free to carry out atrocities unobserved by the wider international community.

At first they largely refrain from doing so, at any rate on a systematic basis (the exception is Poland in 1939-40). After Germany's first conquests in the west, in the summer of 1940, the newly occupied countries (Luxembourg, Netherlands, Belgium, northern France) experience the horrors of an alien police state and the anti-Semitic measures long familiar within Germany. But German rule here is less brutally repressive than in the east. And the explanation lies in Hitler's theories.

Germans are to rule the united Europe of Hitler's dreams, but they will need assistance. This can only be provided, he believes, by 'Aryans' in the countries to the west of Germany, in those regions settled in the distant past by Germanic peoples such as Franks, Goths, Angles, Saxons and Vikings. He expects, ultimately, cooperation from the west. And he likes to emphasize that the future belongs not to a dominant nation, but a dominant race.

By contrast the regions to the east of Germany, inhabited by the Slavs whom he categorizes as Untermenschen ('subhumans'), are suitable only for subjugation. This explains the treatment of the Poles in 1939, and the sudden gear-change in German brutality with the invasion of Russia in 1941.

German treatment of Russian prisoners of war symbolizes the change. On June 27, five days after the invasion, the town of Minsk is surrounded. More than 100,000 Russian soldiers are captured and are herded into open fields, surrounded by barbed wire and armed guards. They are given no food, and so over the next few weeks they starve to death. When winter comes, hundreds of thousands of Russian prisoners captured elsewhere on the front are even more easily got rid of. They freeze.

Subsequently the Germans realize that this policy is losing them a valuable reserve of slave labour. It is better that such people should die working for the Reich. In a speech to SS leaders Himmler emphasizes that there is no need to be concerned about 'What happens to a Russian'.

The invasion of Russia provides the same turning point in the German treatment of the Jews. In planning the campaign, Hitler and Himmler set up four Einsatzkommando (Special Task Commandos) to follow in the wake of the army. The special task for these SS men is to exterminate two groups of people, the most potent figures in Hitler's demonology, Communist officials and Jews.

The work is carried out with ruthless efficiency. Victims are rounded up in villages and towns, are herded into the countryside, are forced to dig long trenches and then are machine-gunned to fall into the ready-made graves. Within the first few weeks of the German presence in Russia tens of thousands of Jews are murdered in this systematic way. It is the beginning of the Holocaust.

The Holocaust: 1941-1942

The term holocaust, originally meaning a sacrifice consumed by fire in a Greek temple, has been used since the early 19th century for the murder of a large number of people. In recent decades it has acquired a much more specific significance. It now defines, almost exclusively, the systematic attempt by Hitler and the Nazis to exterminate the Jewish people. In the 20th century, which far outstripped all others in the horrors perpetrated by humans on their own kind, the Holocaust has come to stand as the defining atrocity.

It is also the atrocity, in the whole of world history, most deliberately planned as the fulfilment of a theory. A flawed and fanatic theory, but one of fatal potency.

The theory, articulated by Hitler in Mein Kampf and in frequent ranting speeches, taps into a deep-rooted European tradition of anti-Semitism, blends in some 19th-century fantasies about ethnic identity and racial purity, and finally adds a dash of 20th-century neurosis about socialism. The troubles of Germany and Austria are thereby blamed on a conspiracy of Jews , working like a virus in all spheres of national life to take over the economy and even, through sexual intermingling, to degrade the pure Aryan stock.

The misfortune underlying the tragedy of the Holocaust is that someone with these views succeeds in becoming the leader of a powerful nation and then, for a brief while, the conqueror of Europe.

From achieving power in 1933 until the outbreak of war in 1939 (an event for which he holds the Jews responsible), Hitler's ambition is to rid Germany and Austria of the nations' long-resident Jews by making them move elsewhere. But with his invasion of Russia in 1941 he begins to conceive a more drastic outcome. The 'final solution of the Jewish problem' (a phrase used in Nazi documents from early in 1942) will be death.

Within the first few days of the Russian campaign Hitler's Special Task forces round up and shoot large numbers of Jews. In two weeks of continual executions in early July, in the city of Kishinev alone, one such task force kills 10,000 people.

On June 27, in Bialystok, German soldiers chase Jews through the narrow streets around a blazing synagogue, like devils in a medieval scene of the Last Judgement. Hundreds of Jews have been locked into the synagogue before it is set on fire. Once it is blazing, the doors are broken down and others are shoved into the cauldron.

But the Nazis are already working on a less visible and more efficient method of achieving their purpose. It is first employed at Chelmno, in Poland, during 1941. Three vans are specially adapted for the killing of people through exposure to lethal gas. During the first six months 97,000 Jews die in these vans. The scheme is considered highly successful. So steps are taken to provide larger-scale death camps with permanent buildings.

These death camps are built on Polish or Russian soil. One of the first and largest is Treblinka (in Poland) where more than 750,000 Jews are killed during 1942, most of them brought there from the Warsaw ghetto.

The placing of the concentration camps in the east, relatively out of sight, is a practical measure of discretion by the Nazi high command. On 20 January 1942 a meeting is convened at Wannsee, a lakeside villa near Berlin, by Himmler's second-in-command in the SS, Reinhard Heydrich. Heydrich has been put in charge of the 'final solution'. The purpose of the meeting is to discuss the practical arrangements.

It is taken for granted by now in these high Nazi circles that the solution must apply to Jews in all the nations occupied by the Germans. But death camps in France or the Netherlands will be more exposed to view. So it is decided that Jews from such countries must be brought to the Polish camps.

Thus begins one of the abiding images of the holocaust - trains of cattle trucks into which Jews are crowded, heading for an unknown destination. The programme is described as 'transportation of the Jews towards the Russian East'. Early in 1942 the prospect facing these people is immediate death. But later there are two possibilities - immediate death by gas, or slow death by hard labour and deprivation.

The Holocaust: 1942-1945

During 1942 it occurs to the Nazis that, as with the Soviet prisoners of war, they are wasting valuable slave labour in their policy of automatic murder of the Jews. So a new form of camp is planned in which those on the trains will be classified, on arrival, as 'fit' or 'unfit' to work. The fit go one way, to the prison huts where they will live for a while as unpaid and underfed labourers. The unfit go the other way, to the gas chambers.

The first camp of this kind, ready for use in March 1942, is built at Auschwitz in Poland. An unknown number of people (certainly well in excess of a million) die in this camp in the next three years. More than half of them - the unfit, the elderly, the children - are killed in the four gas chambers within a day or two of their arrival.

Those judged fit 'to be worked to death' (a phrase used by Himmler) are put to the service of Germany's war production. Factories are moved from the vulnerable Ruhr, in the west, to the neighbourhood of Auschwitz - beyond the range of Allied bombers. Several of Germany's great industrial enterprises tarnish their reputation by benefiting during these years from Jewish slave labour.

By the end of 1942 knowledge of what is going on is not limited to those actively involved on the German side. On December 17 Anthony Eden tells the House of Commons in London that reliable reports have been received 'regarding the barbarous and inhuman treatment to which Jews are being subjected in German-occupied Europe'.

Eden is putting before the House an international declaration, published on that day, which is more direct in its account of what is actually going on. Issued jointly by the USA, the USSR, Great Britain and the governments in exile of nine occupied European countries, the declaration condemns in the strongest possible terms Germany's 'bestial policy of cold-blooded extermination'.

This is straightforward language, in stark contrast to the terms used in Nazi documents about a solution to the Jewish question and journeys to the east. But it is this veil of German euphemism which has enabled a few extreme right-wing historians to argue the preposterous theory that Hitler did not know what the terms meant and so was perhaps personally unaware of the Holocaust.

Although by far the largest group of victims to die because of Hitler's theories (about 6 million), the Jews are not alone. Gypsies too are considered a polluting threat to an Aryan society. Rounded up and sent to the camps, most of them are marked down for Sonderhandlung ('special treatment' - another Nazi euphemism, meaning murder). It is calculated that in all some 400,000 Gypsies are killed.

Even 'Aryans' are not immune from the obsession with purity and perfection. In 1939 Hitler signs an ultra-secret decree authorising the death of any German judged 'incurably ill'. This covers mental illness, and the victims (probably about 100,000 in the next two years) are later described as 'useless defectives'. They too should be considered victims of the Holocaust.

Fighting on four fronts: 1944

Since 1941 Stalin has in vain urged the Allies to open up a new front in the west to relieve German pressure on Russia. Now finally, by 1944, he is supported on two other fronts - both of them directly threatening the Nazi heartlands of Germany and Austria.

From November 1943 the Allies are pushing north in an Italy now hostile to Germany, though it is nine months before they reach Florence and not until the spring of 1945 that they make any further progress. More effective by far is the second front, the one which Stalin always had in mind - an attack through France and Belgium aimed directly at Germany's industrial base in the Ruhr.

The British and American landings in Normandy take place in June 1944. Initial progress is slow, but Paris is liberated in August and Brussels in September. Thereafter there is another long delay caused by an Allied failure to cross the Rhine (at Arnhem) and a German counter-attack (battle of the Bulge).

Meanwhile the Russians have been making rapid progress on the original front, in the east. They advance steadily from January 1944, and by early 1945 Russian forces are in control of Poland, Rumania and Bulgaria. And on a fourth front, at home, German cities have been suffering the Blitz previously inflicted on Britain. Berlin is bombed almost nightly from November 1943. Dresden is flattened in February 1945.

The noose tightens: 1945

During the spring of 1945 the collapse of Germany comes, after so long, with surprising speed. German commanders in the field, no longer feeling any enthusiasm for a fight which is clearly lost, begin to disregard the stream of hysterical instructions from Hitler to stand firm whatever the cost. To the armies defending the Rhine his order includes the statement that the battle shall be conducted 'without consideration for our own population'.

A scorched earth policy within Germany is now the order of the day. All public utilities in the path of the Allies (water, gas, electricity) are to be destroyed. To protests from within his inner group, Hitler replies that if the war is lost, the German nation is lost. There is no need to consider the future requirements of a vanquished people.

In this situation, and with Hitler's final reserves sent to the eastern front, the Allies meet little opposition when they cross the Rhine at various points on March 22-4 (first the Third US Army led by George Patton in the south, followed by the British and Canadians in the north). Both groups, pressing on east, reach the Elbe in mid-April. On the way they discover the horrors which bring home to the west, more powerfully than ever before, the true nature of the Nazi regime.

On April 10 the Americans reach the concentration camp at Buchenwald. Five days later the British come across Belsen, where there are 35,000 unburied bodies and as many emaciated prisoners still just alive. And these are not even the death camps - merely places where prisoners are subjected to hard work, little food and Nazi indifference.

Meanwhile the Russians, pushing westwards, have entered Vienna on April 6. Within three weeks, by April 25, they reach and encircle Berlin, where Hitler is at last beginning to recognize that there can be no miraculous outcome.

News of the death of Roosevelt, on April 12, has been enough to make him hope for a sudden reversal of fortune. But on April 29, against his specific orders, the German army in Italy surrenders to the Allies. Hitler also knows that Himmler, his trusted SS commander, has been making peace overtures behind his back. Livid with anger at this betrayal, he now recognizes the end and prepares to meet it. In the elaborate bunker beneath the Chancellery he puts his affairs in order.

The traitor Himmler is formally expelled from the party. Admiral Dönitz is appointed as Hitler's successor and the names of his cabinet are selected. Hitler then retires for a while to dictate his last will and testament, a tract of self-justification in which the Jews are still blamed for the war and the Nazi party is urged to continue the necessary campaign against them.

On this same day, April 29, in the early hours of the morning, Hitler rewards a woman who has always been quietly faithful to him. He marries his mistress, Eva Braun, following the ceremony with a small champagne party at which Goebbels (the Nazi minister of propaganda) and Martin Bormann (Hitler's secretary and close adviser) are the principal guests.

On April 30 Hitler holds his usual daily conference while the Russians, in the streets above, are only two blocks away from the Chancellery. Then Hitler and Eva Braun retire to their quarters. She takes poison, he shoots himself in the mouth. On the following day Goebbels orders SS men to give his six children lethal injections and to shoot his wife and himself.

Hitler was appalled that his nation had surrendered in World War I without a single foreign soldier setting foot on German soil. His own unbreakable resolve results in the opposite extreme. When he dies, the enemy is in the heart of Berlin. A week later, on May 7, the unconditional surrender of all the German forces is signed at General Eisenhower's headquarters. May 8 is celebrated by the Allies as V-E Day - victory in Europe.